W. A. Rogers—New Diffraction Ruling Engine. 55 
an inch. Hach half will then have an error of one twenty- 
thousandth of an inch. But this maximum value is made u 
of successive increments of very minute errors, starting wit 
the zero of revolution. If the graduations are ten thousand to 
the inch, there will be five hundred spaces in half a revolution 
of the screw. This maximum value, then, of the twenty- 
thousandth of an inch, a quantity easily measured, will be 
made up of five hundred additions of the errors of the succes- 
sive individual spaces. If the error is a constant one for each 
space, its value will therefore be only one ten millionths of an 
inch, a quantity far beyond the ultimate limits of measurement 
with the microscope. When, by one hundred successive addi- 
tious, the error amounts to one hundred thousandths of an inch, 
it will then be barely within the limits of detection. 
In Mr. Rutherfurd’s screw the errors of this class are nearly 
overcome by giving an excentricity to the index of the screw, 
sufficient to neutralize them at the quadrant points of revo- 
lution; that they are not entirely eliminated is shown not 
only by the actual measurement of distant lines, especially at 
the octant points of revolution, but also by the fact that the sur- 
face-waves, resulting from the residual systematic errors, are 
easily seen with the unaided eye when the gratings are exam- 
ined with a monochromatic flame. 
In the investigations of the wave lengths of light hitherto 
made, no attention has been paid to the periodic errors 
which are a function of one revolution of the ruling-screw. 
Our present knowledge of wave lengths depends on the suppo- 
sition that the gratings from which they were determined are 
homogeneous throughout their whole extent. If I am not mis- 
taken, both Angstrém and Van der Willigen, who have done 
the best work in this direction, obtained the value of one inter- 
val by dividing the distance between the end lines by the num- 
ber of spaces. It is at least. possible that the error introduced 
through the neglect to take into account the varying pitch of 
the screw, may be of appreciable magnitude. I can now only 
hote in this connection, that when oil or grease is used as a 
lubricant, the curve which represents the periodic errors usually 
a grating homogeneous throughout its whole extent. Int 
execution of this work I was more than fortunate in securing 
